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    <td width="40"><a href="ChEq_0_Contents.htm"><img src="images/Book.gif" alt="" border="0" width="32" height="32"></a>&nbsp;</td>
    <td align="left"><a href="ChEq_0_Contents.htm">Chemical Equilibria</a></td>
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<center><h2></a>What are chemical equilibria?</h2></center>

<p><b>Chemical equilibrium</b> is the state of a reaction system in which the
rate of product formation equals the rate of product decomposition.
The <b>equilibrium constant</b> (or <b>formation constant</b>),
<i>K</i>, is equal to the ratio between the forward and reverse rate constants.
Equilibrium constants depend on temperature, pressure, ionic strength (for aqueous solutions), etc,
and can be determined from:</p>
<ul>
<li>kinetic experiments (concentrations <i>versus</i> time),</li>
<li>equilibrium measurements (emf, spectrophotometry, etc),</li>
<li>thermodynamic calculations <nobr>(&#916;<i>G</i><sub>r</sub></nobr> =
    <nobr>&#8722;<i>RT</i>&nbsp;ln<i>K</i>).</nobr></li>
</ul>
<p>There are many literature <a href="ChEq_Sources_logK.htm">sources of equilibrium constants</a> and of <a href="ChEq_Sources_Data.htm">thermodynamic data</a></p>

<p>A <b>global reaction</b> is the <i>sum</i> of single-step reactions.
The following table shows an example with two reactions between a central group,
M (for example a metal ion) and a ligand L:

<table width="390" border="0">
<tr valign="top"><td>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</td>
<td width="44%">M + L <img src="images/rlh.gif" alt="=" border="0" width="14" height="10"> ML<br>
ML + L <img src="images/rlh.gif" alt="=" border="0" width="14" height="10"> <nobr>ML<sub>2</sub></nobr>
</td>
<td width="56%">(single-step reactions)</td>
</tr>
<tr valign="top"><td>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</td>
<td width="44%">M + 2 L <img src="images/rlh.gif" alt="=" border="0" width="14" height="10"> <nobr>ML<sub>2</sub></nobr></td>
<td width="56%">(global reaction)</td>
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</table>

ML, <nobr>ML<sub>2</sub>,</nobr> etc, are called <b>complexes.</b> Originally they were called complex ions, but also neutral aqueous species may be complexes.</p>

<p>The equilibrium constant for the global reaction is often denoted by the Greek letter &#147;beta&#148;
<nobr>(&#946;<sub>2</sub></nobr> for the last reaction listed above).
The equilibrium constant for the global reaction
is equal to the <i>product</i> of the single-step reactions:</p>
<table width="390" border="0">
<tr valign="top"><td>&nbsp;&nbsp;&nbsp;&nbsp;</td>
<td width="40%"><p>M + L <img src="images/rlh.gif" alt="=" border="0" width="14" height="10">
    ML</p></td>
<td width="60%"><p><nobr><i>K</i><sub>1</sub> = [ML]/([M][L])</nobr></p></td>
</tr>
<tr valign="top"><td>&nbsp;</td>
<td><p>ML + L <img src="images/rlh.gif" alt="=" border="0" width="14" height="10">
    <nobr>ML<sub>2</sub></nobr></p></td>
<td><p><nobr><i>K</i><sub>2</sub> = [ML<sub>2</sub>]/([ML][L])</nobr></p></td>
</tr>
<tr valign="top"><td>&nbsp;</td>
<td><p>M + 2 L <img src="images/rlh.gif" alt="=" border="0" width="14" height="10">
        <nobr>ML<sub>2</sub></nobr></p></td>
<td><p><nobr>&#946;<sub>2</sub></nobr>  = <nobr>[ML<sub>2</sub>]/([M][L]<sup>2</sup>)</nobr></p>
  <p><nobr>&#946;<sub>2</sub></nobr> = <nobr><i>K</i><sub>2</sub> <i>K</i><sub>1</sub></nobr></p>
  <p><nobr>log&nbsp;&#946;<sub>2</sub></nobr> = <nobr>log&nbsp;<i>K</i><sub>1</sub></nobr>
      <nobr>+&nbsp;log&nbsp;<i>K</i><sub>2</sub></nobr></p></td>
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</table>

<p>To draw an equilibrium diagram you need:</p>
<ul>
<li>the values for the equilibrium constants,
<li>the stoichiometric coefficients for the corresponding reactions,
<li>constraints on total concentrations, etc.
</ul>

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